63.1.110 problem 157

Internal problem ID [15550]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 157
Date solved : Thursday, October 02, 2025 at 10:19:47 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 y+y^{\prime \prime }&=2 \sin \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)+4*y(x) = 2*sin(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (2 c_1 -x \right ) \cos \left (2 x \right )}{2}+\sin \left (2 x \right ) c_2 \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 62

ode=D[y[x],{x,2}]+4*y[x]==2*Sin[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sin (2 x) \int _1^x\frac {1}{2} \sin (4 K[2])dK[2]+\cos (2 x) \int _1^x-\sin ^2(2 K[1])dK[1]+c_1 \cos (2 x)+c_2 \sin (2 x) \end{align*}

✓ Sympy. Time used: 0.058 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) - 2*sin(2*x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} \sin {\left (2 x \right )} + \left (C_{1} - \frac {x}{2}\right ) \cos {\left (2 x \right )} \]